Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
To determine which of the given expressions are equivalent to [tex]\( x^{9/4} \)[/tex], we need to see if we can rewrite each expression to match [tex]\( x^{9/4} \)[/tex].
Let's analyze each expression step-by-step:
Expression A: [tex]\(\left(x^4\right)^{1 / 9}\)[/tex]
- Rewriting this expression using the power of a power rule [tex]\((a^m)^n = a^{mn}\)[/tex], we get:
[tex]\[ \left(x^4\right)^{1 / 9} = x^{4 \cdot (1 / 9)} = x^{4/9} \][/tex]
This is not equivalent to [tex]\( x^{9/4} \)[/tex].
Expression B: [tex]\((\sqrt[4]{x})^9\)[/tex]
- Rewriting [tex]\(\sqrt[4]{x}\)[/tex] as [tex]\( x^{1/4} \)[/tex], we get:
[tex]\[ (\sqrt[4]{x})^9 = (x^{1/4})^9 = x^{(1/4) \cdot 9} = x^{9/4} \][/tex]
This is equivalent to [tex]\( x^{9/4} \)[/tex].
Expression C: [tex]\(\sqrt[9]{x^4}\)[/tex]
- Rewriting [tex]\(\sqrt[9]{x^4}\)[/tex] as [tex]\( (x^4)^{1/9} \)[/tex], we get:
[tex]\[ \sqrt[9]{x^4}= (x^4)^{1/9} = x^{4 \cdot (1/9)} = x^{4/9} \][/tex]
This is not equivalent to [tex]\( x^{9/4} \)[/tex].
Expression D: [tex]\(\sqrt[4]{x^9}\)[/tex]
- Rewriting [tex]\(\sqrt[4]{x^9}\)[/tex] as [tex]\( (x^9)^{1/4} \)[/tex], we get:
[tex]\[ \sqrt[4]{x^9} = (x^9)^{1/4} = x^{9 \cdot (1/4)} = x^{9/4} \][/tex]
This is equivalent to [tex]\( x^{9/4} \)[/tex].
Expression E: [tex]\((x^9)^{1 / 4}\)[/tex]
- Rewriting [tex]\((x^9)^{1 / 4}\)[/tex] using the power of a power rule, we get:
[tex]\[ (x^9)^{1/4} = x^{9 \cdot (1/4)} = x^{9/4} \][/tex]
This is equivalent to [tex]\( x^{9/4} \)[/tex].
Expression F: [tex]\((\sqrt[3]{x})^4\)[/tex]
- Rewriting [tex]\(\sqrt[3]{x}\)[/tex] as [tex]\( x^{1/3} \)[/tex], we get:
[tex]\[ (\sqrt[3]{x})^4 = (x^{1/3})^4 = x^{(1/3) \cdot 4} = x^{4/3} \][/tex]
This is not equivalent to [tex]\( x^{9/4} \)[/tex].
So, the expressions that are equivalent to [tex]\( x^{9/4} \)[/tex] are:
- Expression B: [tex]\((\sqrt[4]{x})^9\)[/tex]
- Expression D: [tex]\(\sqrt[4]{x^9}\)[/tex]
- Expression E: [tex]\((x^9)^{1 / 4}\)[/tex]
Therefore, the correct answers are B, D, and E.
Let's analyze each expression step-by-step:
Expression A: [tex]\(\left(x^4\right)^{1 / 9}\)[/tex]
- Rewriting this expression using the power of a power rule [tex]\((a^m)^n = a^{mn}\)[/tex], we get:
[tex]\[ \left(x^4\right)^{1 / 9} = x^{4 \cdot (1 / 9)} = x^{4/9} \][/tex]
This is not equivalent to [tex]\( x^{9/4} \)[/tex].
Expression B: [tex]\((\sqrt[4]{x})^9\)[/tex]
- Rewriting [tex]\(\sqrt[4]{x}\)[/tex] as [tex]\( x^{1/4} \)[/tex], we get:
[tex]\[ (\sqrt[4]{x})^9 = (x^{1/4})^9 = x^{(1/4) \cdot 9} = x^{9/4} \][/tex]
This is equivalent to [tex]\( x^{9/4} \)[/tex].
Expression C: [tex]\(\sqrt[9]{x^4}\)[/tex]
- Rewriting [tex]\(\sqrt[9]{x^4}\)[/tex] as [tex]\( (x^4)^{1/9} \)[/tex], we get:
[tex]\[ \sqrt[9]{x^4}= (x^4)^{1/9} = x^{4 \cdot (1/9)} = x^{4/9} \][/tex]
This is not equivalent to [tex]\( x^{9/4} \)[/tex].
Expression D: [tex]\(\sqrt[4]{x^9}\)[/tex]
- Rewriting [tex]\(\sqrt[4]{x^9}\)[/tex] as [tex]\( (x^9)^{1/4} \)[/tex], we get:
[tex]\[ \sqrt[4]{x^9} = (x^9)^{1/4} = x^{9 \cdot (1/4)} = x^{9/4} \][/tex]
This is equivalent to [tex]\( x^{9/4} \)[/tex].
Expression E: [tex]\((x^9)^{1 / 4}\)[/tex]
- Rewriting [tex]\((x^9)^{1 / 4}\)[/tex] using the power of a power rule, we get:
[tex]\[ (x^9)^{1/4} = x^{9 \cdot (1/4)} = x^{9/4} \][/tex]
This is equivalent to [tex]\( x^{9/4} \)[/tex].
Expression F: [tex]\((\sqrt[3]{x})^4\)[/tex]
- Rewriting [tex]\(\sqrt[3]{x}\)[/tex] as [tex]\( x^{1/3} \)[/tex], we get:
[tex]\[ (\sqrt[3]{x})^4 = (x^{1/3})^4 = x^{(1/3) \cdot 4} = x^{4/3} \][/tex]
This is not equivalent to [tex]\( x^{9/4} \)[/tex].
So, the expressions that are equivalent to [tex]\( x^{9/4} \)[/tex] are:
- Expression B: [tex]\((\sqrt[4]{x})^9\)[/tex]
- Expression D: [tex]\(\sqrt[4]{x^9}\)[/tex]
- Expression E: [tex]\((x^9)^{1 / 4}\)[/tex]
Therefore, the correct answers are B, D, and E.
B and D and E
B = (c^1/4)^9 = x^9/4
D = (x^9*1/4) = x^9/4
E = (x^9)^1/4 = x^9/4
B = (c^1/4)^9 = x^9/4
D = (x^9*1/4) = x^9/4
E = (x^9)^1/4 = x^9/4
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.